This is the Part 3 of my series of tutorials about the math behind Support Vector Machine.

If you did not read the previous articles, you might want to take a look before reading this one :

### SVM - Understanding the math

Part 1: What is the goal of the Support Vector Machine (SVM)?

Part 2: How to compute the margin?

**Part 3: How to find the optimal hyperplane?**

Part 4: Unconstrained minimization

Part 5: Convex functions

Part 6: Duality and Lagrange multipliers

## What is this article about?

The main focus of this article is to show you the reasoning allowing us to select the optimal hyperplane.

Here is a quick summary of what we will see:

- How can we find the optimal hyperplane ?
- How do we calculate the distance between two hyperplanes ?
- What is the SVM optimization problem ?

## How to find the optimal hyperplane ?

At the end of Part 2 we computed the distance between a point and a hyperplane. We then computed the margin which was equal to .

However, even if it did quite a good job at separating the data it was not the *optimal* hyperplane.